Tinh nhanh
(2013 nhan 2014 nhan 2015) nhan (1-1/3-1/2-1/6)
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\(=\frac{1}{5}\times\frac{1}{3}\times\frac{3}{7}\times\frac{1}{2}\)
\(=\left(\frac{1}{5}\times\frac{1}{2}\right)\times\left(\frac{1}{3}\times\frac{3}{7}\right)\)
\(=\frac{1}{10}\times\frac{1}{7}\)
\(=\frac{1}{70}\)
\(\left(1-\frac{1}{2}\right)\times\left(1-\frac{1}{3}\right)\times\left(1-\frac{1}{4}\right)\times\left(1-\frac{1}{5}\right)...\times\left(1-\frac{1}{100}\right)\)
=\(\frac{1}{2}\times\frac{2}{3}\times\frac{3}{4}\times\frac{4}{5}\times...\times\frac{99}{100}\)
=\(\frac{1\times2\times3\times4\times...\times99}{2\times3\times4\times5\times...\times100}\)
= \(\frac{1}{100}\)
\(\left[12\cdot15-x\right]\cdot\frac{1}{4}=120\cdot\frac{1}{4}\)
\(\Leftrightarrow\left[180-x\right]\cdot\frac{1}{4}=30\)
\(\Leftrightarrow180-x=30:\frac{1}{4}\)
\(\Leftrightarrow180-x=120\)
\(\Leftrightarrow x=60\)
\(\frac{2015\cdot2017-1}{2014+2015\cdot2016}\)\(\cdot\frac{2}{3}\)
\(=\frac{2015\cdot\left(2016+1\right)-1}{2014+2015\cdot2016}\cdot\frac{2}{3}\)
\(=\frac{2015\cdot2016+\left(2015-1\right)}{2014+2015\cdot2016}\cdot\frac{2}{3}\)
\(=\frac{2015\cdot2016+2014}{2014+2015\cdot2016}\cdot\frac{2}{3}\)
\(=1\cdot\frac{2}{3}\)
\(=\frac{2}{3}\)
Bạn dùng công thức này mà làm nhé :\(\frac{n}{a\times\left(a+n\right)}=\frac{1}{a}-\frac{1}{a+n}\)
Ví dụ :\(\frac{2}{3\times5}=\frac{1}{3}-\frac{1}{5};\frac{3}{4\times7}=\frac{1}{4}-\frac{1}{7};\frac{5}{6\times11}=\frac{1}{6}-\frac{1}{11}\)
\((2013\cdot2014\cdot2015)\cdot(1-\frac{1}{3}-\frac{1}{2}-\frac{1}{6})\)
\(=(2013\cdot2014\cdot2015)\cdot(\frac{6}{6}-\frac{2}{6}-\frac{3}{6}-\frac{1}{6})\)
\(=(2013\cdot2014\cdot2015)\cdot(\frac{6-2-3-1}{6})\)
\(=(2013\cdot2014\cdot2015)\cdot0=0\)
( 2013 × 2014 × 2015 ) × ( 1 - 1/3 - 1/2 - 1/6 )
= ( 2013 × 2014 × 2015 ) × ( 6/6 - 2/6 - 3/6 - 1/6)
= ( 2013 × 2014 × 2015 ) × 6 - 2 - 3 - 1/6
= ( 2013 × 2014 × 2015 ) × 0
= 0